In this paper, we only considered the leading-order effect from
integrating out massive degrees of freedom. We did not address the
question of bounds that can be applied to IR-safe observables in four
dimensions, nor have we included the loops of massless particles which
generate more general logarithmic corrections in the low-energy
expansion of the amplitude. We leave these important questions to
future work. The logarithmic running was discussed in
Refs. [1]}, [2]}, [3]},
with the basic idea being that instead of expanding the amplitude
around \(s,t=0\)  one considers dispersive representations of the EFT
couplings defined at some scale. To deal with the IR divergences we
may consider dressed states (see e.g.
Ref. [4]}, [5]} for a recent
discussion), for which the full implications of unitarity and crossing
are still to be fully understood. Another interesting problem is to
repeat the analysis of the present paper in the context of \(\rm AdS_4/CFT_3\)  where the problem of IR divergences does not arise, but
dispersive techniques discussed in the present paper still
hold [6]}.
